In the present article, we aim at filling this gap by a systematic
study of two paradigmatic stochastic processes that can exhibit
anomalous diffusion, one being Markovian, the other being
non-Markovian. Both of these processes involve Gaussian noise, yet
non-trivial (in one case non-Markovian) noise correlation
functions. Also, we do not impose a priori the presence of the
FDR, thereby considering systems which have been called "athermal"
[1]}. For these two exemplary processes, we systematically
apply the framework of "standard" ST focusing, in particular, on
definitions of heat, medium and total entropy production, and the IFR.
